20105

Atlantic DLI Workshop

Survivor’s Training in Statistics An Assessment of Knowledge You likely have taken at least one statistics course in your undergraduate or graduate training. The relevance of statistics may not have been apparent to you when you were studying it and consequently, you may feel that your knowledge of statistics is rusty. I suspect, however, that you know more statistics than you realize. Some people lack confidence in their knowledge of statistics because they have not connected what they do know about statistics with their work and life. This exercise will help you assess some fundamental knowledge of statistics. On the basis of this outcome, we’ll talk about a framework for thinking about statistics that hopefully adds relevance to your knowledge. You may also discover areas in statistics that you would like to learn more about as a result of this assessment. Some references will be provided to help you pursue this through individual study. I. It’s about organizing and measuring. The following questions require the use of Table 1: Average undergraduate tuition fees for full-time students, by discipline, by provinces, which can be found in the handout accompanying this document. 1. Using this table’s title, identify the characteristics being described in this table. a. b. c. d. For extra credit, what characteristic is included in the table but not mentioned in the title: e. These characteristics (known as variables) have qualitative and/or quantifiable values. These values depend upon how a variable has been defined and measured. 2. What level of measurement is associated with Discipline? 3. In the table, how are the values of Academic Year utilized? 4. What level of measurement is used with Academic Year? 5. What is the metric or unit of measure of the values in the 60 cells created by combining the categories of Discipline and Academic Year? 6. What factors are used to weight the averages in these cells? 7. For 2003-2004, the average of the 12 disciplines in the table is 6,335. Why does the table show the total undergraduate average for this academic year to be 5,557?

C. Humphrey

1

Atlantic DLI Workshop

2005

Acadia University

8. For extra credit, from what unit of observation would you assume the data was collected to produce this table? II. Indicators. The following questions require the use of Table 2: Economic Indicators, by provinces and territories (monthly and quarterly). For the following indicators listed for New Brunswick, indicate its metric, that is, the units in which the value appears. Indicator

Metric

9 Employment 10. Unemployment rate 11. Participation rate 12. Labour income 13. Average weekly earnings 14. Consumer price index 15. Building permits 16. Housing starts

III. Rates and Indexes. The following questions require the use of Table 3: Births and birth rate, by provinces and territories and Table 4: Estimates of population, by Canada and Atlantic provinces. 17. What do the numbers in the cells of Table 3 represent? 18. Why are the years overlapping? For example 1999-2000 and 2000-2001. 19. What was the number of births in Newfoundland and Labrador in 2003-2004? 20. What was the number of births in Prince Edward Island in 2003-2004?

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C. Humphrey

Acadia University

20305

Atlantic DLI Workshop

21. Which of these two provinces appears to have the larger birth rate in 2003-2004? 22. What do the numbers in the cells of Table 4 represent? 23. Do the population estimates overlap a calendar year? You will need to calculate the crude birth rate for PEI and Newfoundland to compare their birth rate in 2003-2004. The crude birth rate is calculated by dividing the number of births by the population of the province and multiplying this proportion by 1000. This calculation provides a birth rate per 1000 population. Even though the number of births and population estimates do not completely align by calendar year, use these figures to calculate approximate rates. (After completing this, you might want to go online to the Statistics Canada website at http://www.statcan.ca/english/Pgdb/demo04a.htm and select Birth rate to compare your estimate with the corresponding figures in the table.) 24. What is the crude birth rate for PEI? 25. What is the crude birth rate for Newfoundland and Labrador? 26. Which province had the higher birth rate per 1000 in 2003-2004? IV. It’s about summarizing continuous variables. Moving from published tables, let’s look at output from a public use microdata file available through DLI, the Survey of Financial Security: family economic file, 1999. The following questions require the use of Table 5: Total Government Transfers by Economic Family for Newfoundland in the 1998 tax year (unweighted). 27. Table 5 consists of output from the SPSS Explore procedure containing four parts: a list of summary statistics, the quartiles for this variable, a stem-and-leaf plot, and a boxplot. From the appearance of the summary statistics, what is the level of measurement for the variable GTR27 (government transfers)? 28. What is the mean or average government transfer to the economic families in this sample? 29. What is the median government transfer in this sample (use the Percentiles listing)?

C. Humphrey

3

Atlantic DLI Workshop

2005

Acadia University

30. Using these two summary statistics, would you say that the distribution of government transfers is skewed to the left, skewed to the right or fairly evenly distributed? 31. Looking at the stem-and-left distribution of government transfers, what value is the mode? 32. From the boxplot display, would you say that the middle 50 percent of the data is symmetrically distributed around the median or skewed to the right or left of the median? V. It’s about summarizing categorical variables. The following questions refer to Table 6: Family Financial Forecast by Atlantic Provinces (unweighted). 33. In which province do the majority of families see their financial forecast remaining the same? 34. How is the distribution of New Brunswick different from the other provinces? 35. Which cell has the largest difference between the expected and observed counts? VI. It’s about summarizing differences. The following questions rely on Table 7: Government Transfers by Economic Family by Atlantic Provinces (unweighted). 36. Which of the four provincial distributions of government transfers appears to have the most symmetrical middle 50 percent of the data 37. Why do these distributions not have long whiskers on both ends? 38. Which province appears from the boxplots to be different from the others? 39. Using the 95 percent confidence interval for the means, identify the groups of provinces for which their confidence interval overlaps?

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C. Humphrey

Acadia University

20505

Atlantic DLI Workshop

VI. It’s about summarizing relationships. The following questions use Table 8: Total Family Debt Predicted by Age, Total Net Income, Home Ownership, Credit Card Payment Practices, Family Size and Family Financial Forecast for Atlantic Provinces (unweighted). 40. Which independent variables have significant unstandardized B’s at the .01 level? a. b. c. d. 41. What categories does the constant in the model represent? a. b. c. 42. What is the metric of the B coefficients?

C. Humphrey

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